%5E3-formula-example.jpeg "(a-b)^3 Formula Example")
The (a-b)^3 Formula: Definition, Example, and Explanation
The (a-b)^3 formula is a powerful tool in algebra that allows us to simplify and solve complex expressions. In this article, we will explore the definition, example, and explanation of the (a-b)^3 formula.
What is the (a-b)^3 Formula?
The (a-b)^3 formula is a mathematical formula that expresses the cube of the difference of two variables, a and b. It is defined as:
(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
This formula is a special case of the binomial theorem, which is a mathematical formula for expanding powers of a binomial expression.
Example of the (a-b)^3 Formula
Let's consider an example to illustrate how the (a-b)^3 formula works:
Suppose we want to expand the expression (x-2)^3. Using the (a-b)^3 formula, we can write:
(x-2)^3 = x^3 - 3x^2(2) + 3x(2)^2 - (2)^3
Expanding the expression, we get:
(x-2)^3 = x^3 - 6x^2 + 12x - 8
Therefore, the expanded form of (x-2)^3 is x^3 - 6x^2 + 12x - 8.
Explanation of the (a-b)^3 Formula
The (a-b)^3 formula is derived from the binomial theorem, which states that:
(a+b)^n = a^n + na^(n-1)b + n(n-1)a^(n-2)b^2 + ... + b^n
By substituting a-b for a and b, we can derive the (a-b)^3 formula:
(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
The formula consists of four terms: a^3, -3a^2b, 3ab^2, and -b^3. Each term is obtained by multiplying the previous term by -b and reducing the power of a by 1.
Conclusion
The (a-b)^3 formula is a useful tool for simplifying and solving algebraic expressions. It is derived from the binomial theorem and consists of four terms. By understanding the formula and its application, we can expand and simplify complex expressions with ease.
